The coil, or inductor, has a property which forces us to treat it
differently from resistors and capacitors: its magnetic field. Where a
resistor generates no such field and a capacitor generates an electric
field that remains internal to the capacitor, the coil's magnetic field
extends beyond itself, and can easily overlap the turns of wire in an
adjacent coil.

Because of this, we must deal with two separate concepts when combining
inductors in a circuit. These are known as self-inductance, which
is the inherent inductance of the coil under consideration; and mutual
inductance, which is the inductive effect of magnetic interaction
between two coils.

Mutual inductance behaves just like self-inductance in many ways, and
is defined in the same way. If a change in current of 1 ampere/second in
one coil causes a counter EMF of one volt to be generated in the
other coil, they have a mutual inductance of 1 henry.

When we connect two inductors in series, as shown to the right, we have
the question of whether or not their magnetic fields interact. If not,
then their inductances simply add:

LT = L1 + L2

However, if they are physically placed so that they do exhibit a mutual
inductance, this isn't sufficient. We must include a mutual inductance
where each coil's magnetic field affects the other coil. Furthermore, we
must take into account whether the magnetic fields of the two coils are
aiding each other or opposing each other, since each self-inductance can
be either increased or decreased by the value of the mutual inductance,
designated M. Therefore, we must select one of two equations:

LT = (L1 + M) + (L2 + M)
LT = (L1 - M) + (L2 - M)

Or,

LT = L1 + L2 ± 2M

If you try to connect three or more coils in series, you must take into
account the mutual inductance between each pair of coils. That's three
different mutual inductances for three coils, and six mutual inductances
for four coils.